Day 1 Exercises - PNAWS2019
Martina Pocchiari
1/28/2019
Morning Session Exercises
The dataset you have consists of data from 5000 hypothetical subjects on six variables, each of which has two values: cancer: whether a person has cancer. 0=no, 1=yes. try: how often a person has tried cigarettes during adolescence. 0=not often, 1=often. genes: whether a person has good or bad genes. 0=good, 1=bad. smoke: whether a person is a smoker. 0=no, 1=yes. susceptibility: whether a person is susceptible to smoking addiction. 0=no, 1=yes. fingers: whether a person has yellow-stained fingers. 0=no, 1=yes.
The model is generated using a DAG. Your job is to figure out how the arrows run. You can use two instruments for this purpose: first, you can check whether any two variables are independent, and second, you can check whether any two variables are conditionally independent, given a third.
Checking independence:
To check whether two variables X1 and X2 are independent, you type ‘ind(X1,X2)’. The output gives the contingency table for X1 and X2, the expected contingency table for X1 and X2 under independence, and a test of the null hypothesis that the variables are independent in the population. If p<.05, then the program concludes that the variables are dependent; otherwise that they are independent.
##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 3032 353
## 1 1315 300
##
## *Fitting Model*
##
## 2 iterations: deviation 5.684342e-14
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 2942.919 442.081
## 1 1404.081 210.919
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 60.96208
## p-value= 5.818484e-15
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## Checking conditional independence:
To check whether two variables X1 and X2 are conditionally independent, given X3, you type ‘cind(var1=X1, var2=X2, blocker=X3)’. ‘Blocker’ is the variable you condition on. The output gives separate contingency tables for X1 and X2 for the values of X3, the expected contingency tables for X1 and X2 under conditional independence given X3, and a test of the null hypothesis that X1 and X2 are conditionally independent of X3 in the population. If p<.05, then the program concludes that the variables are conditionally dependent given the blocker; otherwise that they are independent.
##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2517 289
## 1 573 124
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 515 64
## 1 742 176
##
##
## *Fitting Model*
##
## 2 iterations: deviation 1.136868e-13
## 2 iterations: deviation 5.684342e-14
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2475.17556 330.82444
## 1 614.82444 82.17556
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 486.17435 92.82565
## 1 770.82565 147.17435
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 45.65795
## p-value= 1.217591e-10
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.1. Consider the three variables ‘fingers’,’cancer’ and ‘smoke’.
a. Are ‘fingers’ and ‘cancer’ independent?
No, they are not independent.
##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 2723 336
## 1 1624 317
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 2659.4946 399.5054
## 1 1687.5054 253.4946
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 29.32747
## p-value= 6.112303e-08
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## b. Are ‘smoke’ and ‘cancer’ conditionally independent given ‘fingers’?
According to the test, conditional independence of smoke and cancer, given fingers, does not hold.
##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2464 278
## 1 259 58
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 568 75
## 1 1056 242
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 9.094947e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2440.81922 301.18078
## 1 282.18078 34.81922
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 537.98660 105.01340
## 1 1086.01340 211.98660
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 32.92007
## p-value= 7.103914e-08
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.c. Are ‘fingers’ and ‘cancer’ conditionally independent given ‘smoke’?
According to the results, Conditional independence of fingers and cancer, given smoke, holds.
##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2464 278
## 1 568 75
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 259 58
## 1 1056 242
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 5.684342e-14
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2456.05436 285.94564
## 1 575.94564 67.05436
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 258.11455 58.88545
## 1 1056.88545 241.11455
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1.285461
## p-value= 0.5258546
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.d. Are ‘smoke’ and ‘fingers’ conditionally independent given ‘cancer’?
According to the results, fingers and smoke, given cancer, are not conditionally independent.
##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2464 259
## 1 568 1056
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 278 58
## 1 75 242
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1899.2721 823.7279
## 1 1132.7279 491.2721
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 181.6355 154.3645
## 1 171.3645 145.6355
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1760.5
## p-value= 0
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.e. Do any additional checks you want. Which causal paths are consistent with the data for these three variables?
Conditional Independencies:
- genes and cancer, given smoke
- genes and cancer, given susceptibility
- try and cancer, given smoke
- susceptibility and try, given genes
Conditional Dependencies:
- fingers and cancer, given try
- smoke and cancer, given try
- susceptibility and try, given genes
##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1642 187
## 1 1390 166
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 524 128
## 1 791 172
##
##
## *Fitting Model*
##
## 2 iterations: deviation 2.842171e-14
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1638.2653 190.7347
## 1 1393.7347 162.2653
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 530.8854 121.1146
## 1 784.1146 178.8854
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.9801407
## p-value= 0.6125833
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1724 246
## 1 408 59
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 442 69
## 1 1773 279
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1723.44686 246.55314
## 1 408.55314 58.44686
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 441.61725 69.38275
## 1 1773.38275 278.61725
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.0104423
## p-value= 0.9947925
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2517 289
## 1 573 124
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 515 64
## 1 742 176
##
##
## *Fitting Model*
##
## 2 iterations: deviation 1.136868e-13
## 2 iterations: deviation 5.684342e-14
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2475.17556 330.82444
## 1 614.82444 82.17556
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 486.17435 92.82565
## 1 770.82565 147.17435
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 45.65795
## p-value= 1.217591e-10
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1390 580
## 1 352 159
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 325 142
## 1 1436 616
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 0
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1383.2084 586.7916
## 1 358.7916 152.2084
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 326.4736 140.5264
## 1 1434.5264 617.4736
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.5673124
## p-value= 0.7530255
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1534 436
## 1 362 105
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 295 216
## 1 1194 858
##
##
## *Fitting Model*
##
## 2 iterations: deviation 4.547474e-13
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1532.6713 437.3287
## 1 363.3287 103.6713
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 296.8705 214.1295
## 1 1192.1295 859.8705
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.06212018
## p-value= 0.9694173
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1512 230
## 1 1294 467
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 317 422
## 1 262 496
##
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1395.3902 346.6098
## 1 1410.6098 350.3902
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 285.8257 453.1743
## 1 293.1743 464.8257
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 110.0298
## p-value= 1.280375e-24
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2269 537
## 1 473 106
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 145 552
## 1 172 746
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2272.9843 533.0157
## 1 469.0157 109.9843
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 136.8105 560.1895
## 1 180.1895 737.8105
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1.286139
## p-value= 0.5256764
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 2723 336
## 1 1624 317
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 2659.4946 399.5054
## 1 1687.5054 253.4946
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 29.32747
## p-value= 6.112303e-08
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2160 254
## 1 930 159
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 563 82
## 1 694 158
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 0
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2129.3919 284.6081
## 1 960.6081 128.3919
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 541.5932 103.4068
## 1 715.4068 136.5932
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 21.06569
## p-value= 2.664674e-05
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2464 278
## 1 568 75
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 259 58
## 1 1056 242
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 5.684342e-14
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2456.05436 285.94564
## 1 575.94564 67.05436
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 258.11455 58.88545
## 1 1056.88545 241.11455
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1.285461
## p-value= 0.5258546
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 2166 315
## 1 2181 338
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 2156.9814 324.0186
## 1 2190.0186 328.9814
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 0.5732319
## p-value= 0.4489775
##
##
## *Conclusion*
## Independence of Var1 and Var2 holds.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1724 246
## 1 408 59
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 442 69
## 1 1773 279
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1723.44686 246.55314
## 1 408.55314 58.44686
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 441.61725 69.38275
## 1 1773.38275 278.61725
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.0104423
## p-value= 0.9947925
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1642 187
## 1 1390 166
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 524 128
## 1 791 172
##
##
## *Fitting Model*
##
## 2 iterations: deviation 2.842171e-14
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1638.2653 190.7347
## 1 1393.7347 162.2653
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 530.8854 121.1146
## 1 784.1146 178.8854
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.9801407
## p-value= 0.6125833
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1539 203
## 1 1551 210
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 627 112
## 1 630 128
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1536.620 205.380
## 1 1553.380 207.620
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 620.523 118.477
## 1 636.477 121.523
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.8956594
## p-value= 0.6390135
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 3090 413
## 1 1257 240
##
## *Fitting Model*
##
## 2 iterations: deviation 4.547474e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 3045.5082 457.4918
## 1 1301.4918 195.5082
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 16.09381
## p-value= 6.028065e-05
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2517 289
## 1 515 64
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 573 124
## 1 742 176
##
##
## *Fitting Model*
##
## 2 iterations: deviation 1.136868e-13
## 2 iterations: deviation 9.094947e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2513.38021 292.61979
## 1 518.61979 60.38021
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 567.52632 129.47368
## 1 747.47368 170.52632
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.789687
## p-value= 0.6737855
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1519 196
## 1 613 109
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1571 217
## 1 644 131
##
##
## *Fitting Model*
##
## 2 iterations: deviation 1.136868e-13
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1500.3611 214.6389
## 1 631.6389 90.3611
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1545.2282 242.7718
## 1 669.7718 105.2282
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 16.18017
## p-value= 0.0003065634
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1539 203
## 1 627 112
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1551 210
## 1 630 128
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1520.82709 221.17291
## 1 645.17291 93.82709
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1524.70861 236.29139
## 1 656.29139 101.70861
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 16.41624
## p-value= 0.0002724324
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 2806 697
## 1 579 918
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 2371.531 1131.469
## 1 1013.469 483.531
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 797.4412
## p-value= 1.942639e-175
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1512 230
## 1 317 422
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1294 467
## 1 262 496
##
##
## *Fitting Model*
##
## 2 iterations: deviation 1.136868e-13
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1284.2072 457.7928
## 1 544.7928 194.2072
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1087.7793 673.2207
## 1 468.2207 289.7793
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 825.4535
## p-value= 5.689169e-180
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1552 163
## 1 344 378
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1254 534
## 1 235 540
##
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1334.2799 380.7201
## 1 561.7201 160.2799
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1038.7561 749.2439
## 1 450.2439 324.7561
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 858.0587
## p-value= 4.73061e-187
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 1896 541
## 1 1489 1074
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 1649.849 787.151
## 1 1735.151 827.849
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 225.1269
## p-value= 6.888658e-51
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1552 163
## 1 1254 534
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 344 378
## 1 235 540
##
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1373.7625 341.2375
## 1 1432.2375 355.7625
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 279.2505 442.7495
## 1 299.7495 475.2505
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 285.7444
## p-value= 8.941064e-63
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 2742 317
## 1 643 1298
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 2070.943 988.057
## 1 1314.057 626.943
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 1788.542
## p-value= 0
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2269 145
## 1 537 552
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 473 172
## 1 106 746
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1933.6808 480.3192
## 1 872.3192 216.6808
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 249.4689 395.5311
## 1 329.5311 522.4689
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1499.354
## p-value= 0
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1542 110
## 1 354 431
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1200 207
## 1 289 867
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1285.2655 366.7345
## 1 610.7345 174.2655
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 817.4105 589.5895
## 1 671.5895 484.4105
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1701.273
## p-value= 0
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1486 132
## 1 343 520
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1256 185
## 1 300 778
##
##
## *Fitting Model*
##
## 2 iterations: deviation 1.136868e-13
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1192.7940 425.2060
## 1 636.2060 226.7940
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 890.1135 550.8865
## 1 665.8865 412.1135
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1755.135
## p-value= 0
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 2414 645
## 1 1089 852
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 2143.1354 915.8646
## 1 1359.8646 581.1354
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 290.4742
## p-value= 3.919505e-65
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1300 415
## 1 352 370
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 1114 674
## 1 293 482
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1162.5687 552.4313
## 1 489.4313 232.5687
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 981.5513 806.4487
## 1 425.4487 349.5513
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 295.9662
## p-value= 5.392053e-65
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2269 537
## 1 473 106
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 145 552
## 1 172 746
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2272.9843 533.0157
## 1 469.0157 109.9843
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 136.8105 560.1895
## 1 180.1895 737.8105
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1.286139
## p-value= 0.5256764
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 1742 739
## 1 1761 758
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 1738.1886 742.8114
## 1 1764.8114 754.1886
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 0.05540769
## p-value= 0.8139073
##
##
## *Conclusion*
## Independence of Var1 and Var2 holds.
## ************************************
##
## ##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 1715 722
## 1 1788 775
##
## *Fitting Model*
##
## 2 iterations: deviation 4.547474e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 1707.3622 729.6378
## 1 1795.6378 767.3622
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 0.2226532
## p-value= 0.6370257
##
##
## *Conclusion*
## Independence of Var1 and Var2 holds.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1390 580
## 1 325 142
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 352 159
## 1 1436 616
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 1.136868e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1386.3562 583.6438
## 1 328.6438 138.3562
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 356.4838 154.5162
## 1 1431.5162 620.4838
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.4000669
## p-value= 0.8187034
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 1618 863
## 1 1441 1078
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 1517.8758 963.1242
## 1 1541.1242 977.8758
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 33.82249
## p-value= 6.037696e-09
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1486 343
## 1 1256 300
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 132 520
## 1 185 778
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1481.5710 347.4290
## 1 1260.4290 295.5710
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 127.9777 524.0223
## 1 189.0223 773.9777
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.4146862
## p-value= 0.8127407
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1334 636
## 1 318 149
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 284 227
## 1 1123 929
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1335.4288 634.5712
## 1 316.5712 150.4288
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 280.5217 230.4783
## 1 1126.4783 925.5217
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.1443186
## p-value= 0.9303827
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1534 436
## 1 362 105
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 295 216
## 1 1194 858
##
##
## *Fitting Model*
##
## 2 iterations: deviation 4.547474e-13
## 2 iterations: deviation 2.273737e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1532.6713 437.3287
## 1 363.3287 103.6713
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 296.8705 214.1295
## 1 1192.1295 859.8705
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.06212018
## p-value= 0.9694173
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 1970 511
## 1 467 2052
##
## *Fitting Model*
##
## 2 iterations: deviation 1.136868e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 1209.239 1271.761
## 1 1227.761 1291.239
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 1989.241
## p-value= 0
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1390 352
## 1 325 1436
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 580 159
## 1 142 616
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 852.8490 889.1510
## 1 862.1510 898.8490
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 356.4182 382.5818
## 1 365.5818 392.4182
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1989.585
## p-value= 0
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1534 295
## 1 362 1194
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 436 216
## 1 105 858
##
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1024.4561 804.5439
## 1 871.5439 684.4561
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 218.4099 433.5901
## 1 322.5901 640.4099
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 1907.285
## p-value= 0
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 1715 722
## 1 1788 775
##
## *Fitting Model*
##
## 2 iterations: deviation 4.547474e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 1707.3622 729.6378
## 1 1795.6378 767.3622
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 0.2226532
## p-value= 0.6370257
##
##
## *Conclusion*
## Independence of Var1 and Var2 holds.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1552 1254
## 1 344 235
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 163 534
## 1 378 540
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1571.6916 1234.3084
## 1 324.3084 254.6916
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 233.4842 463.5158
## 1 307.5158 610.4842
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 60.84017
## p-value= 6.147864e-14
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 3032 353
## 1 1315 300
##
## *Fitting Model*
##
## 2 iterations: deviation 5.684342e-14
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 2942.919 442.081
## 1 1404.081 210.919
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 60.96208
## p-value= 5.818484e-15
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2464 278
## 1 259 58
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 568 75
## 1 1056 242
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 9.094947e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2440.81922 301.18078
## 1 282.18078 34.81922
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 537.98660 105.01340
## 1 1086.01340 211.98660
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 32.92007
## p-value= 7.103914e-08
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2464 278
## 1 259 58
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 568 75
## 1 1056 242
##
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 9.094947e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 2440.81922 301.18078
## 1 282.18078 34.81922
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 537.98660 105.01340
## 1 1086.01340 211.98660
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 32.92007
## p-value= 7.103914e-08
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## var2
## var1 0 1
## 0 1829 1556
## 1 652 963
##
## *Fitting Model*
##
## 2 iterations: deviation 0
## 2 iterations: deviation 0
##
## *Predicted frequencies under Independence*
##
## var2
## var1 0 1
## 0 1679.637 1705.363
## 1 801.363 813.637
##
##
## *Results*
## Likelihood-Ratio ( df = 1 ) 82.01747
## p-value= 1.348891e-19
##
##
## *Conclusion*
## Independence of Var1 and Var2 does not hold.
## ************************************
##
## ##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1534 295
## 1 436 216
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 362 1194
## 1 105 858
##
##
## *Fitting Model*
##
## 2 iterations: deviation 2.273737e-13
## 2 iterations: deviation 0
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1452.2894 376.7106
## 1 517.7106 134.2894
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 288.4684 1267.5316
## 1 178.5316 784.4684
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 143.1715
## p-value= 8.141313e-32
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, does not hold.##
## *Contingency Table*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1534 362
## 1 436 105
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 295 1194
## 1 216 858
##
##
## *Fitting Model*
##
## 2 iterations: deviation 1.136868e-13
## 2 iterations: deviation 4.547474e-13
##
## *Predicted frequencies under CI*
##
## , , blocker = 0
##
## var2
## var1 0 1
## 0 1532.6713 363.3287
## 1 437.3287 103.6713
##
## , , blocker = 1
##
## var2
## var1 0 1
## 0 296.8705 1192.1295
## 1 214.1295 859.8705
##
##
##
## *Results*
## Likelihood-Ratio ( df = 2 ) 0.06212018
## p-value= 0.9694173
##
##
## *Conclusion*
## Conditional independence of var1 and var2, given blocker, holds.Afternoon Session Exercises
Conceptual
Suppose the following model is the true data-generating model of nine symptoms
Theoretically, what should the Gaussian graphical model (GGM; a network of partial correlation coefficients) of the nine observed symptoms look like? Plot or draw the expected network (use only the numbers as node labels). Tip: Note that GAD is not observed and thus (a) not in the GGM and (b) not a node we can condition on.
Suppose we only look at assignments that were graded with a 10. Are motivation and difficulty still independent? That is, in these assignments can we now predict the difficulty from motivation or vice versa? Explain your answer. Tip: if a student with a very poor motivation gets a 10, what does that tell us about the difficulty of the assignment?
Motivation and difficulty are now conditionally dependent, because they are common causes to the same consequence. If a student with very poor motivation gets a 10, this tells us that the difficulty of the assignment would be very low.
Markov Random Fields
The data frame bfiData contains the questions of the bfi (Big Five Inventory) data contained in the psych package.
Obtain the weights matrices from qgraph and bootnet by applying the getWmat function to output of both. Confirm that the results are identical (tip: the operator == tests if values in R are equal)
Qplot weight matrix:
## A1 A2 A3 A4 A5
## A1 0.00000000 -0.279043331 -0.146342179 -0.016675805 -0.031967420
## A2 -0.27904333 0.000000000 0.275803470 0.173285222 0.108863452
## A3 -0.14634218 0.275803470 0.000000000 0.156847223 0.269593707
## A4 -0.01667580 0.173285222 0.156847223 0.000000000 0.063737085
## A5 -0.03196742 0.108863452 0.269593707 0.063737085 0.000000000
## C1 0.04029455 -0.037395321 -0.002218315 -0.068371314 0.043116099
## C2 0.05434301 -0.022258789 -0.008485116 0.187764205 -0.047483569
## C3 0.06161982 0.134280799 0.015567540 -0.036279732 0.023230906
## C4 0.10987691 -0.018992835 -0.003489887 0.002421715 -0.010696224
## C5 -0.01805194 0.035434612 -0.012961536 -0.127108242 0.017937730
## E1 0.05594849 -0.041934586 0.024394176 0.019847681 0.036466766
## E2 0.02246095 -0.038003893 -0.025894605 0.042126375 -0.019223313
## E3 0.06396481 -0.035863899 0.179257763 -0.025832709 0.177079886
## E4 0.06885956 0.004022673 0.057364661 0.134580625 0.236851213
## E5 0.06430575 0.163432325 -0.018008474 -0.015764289 0.023352938
## N1 0.04036771 -0.070769952 0.019636070 0.033789221 -0.066313167
## N2 0.05564717 0.046895017 0.026984344 -0.084303811 -0.045068233
## N3 0.03829669 0.013013859 0.007005090 0.052198539 -0.040611203
## N4 -0.03887133 0.006369286 0.013823130 -0.068996270 0.017002220
## N5 -0.05228719 0.080357098 -0.030455274 0.031196672 0.043848519
## O1 0.07613941 0.027371771 -0.012405364 0.001681125 -0.002893784
## O2 0.04409243 0.051742469 -0.002517178 0.023529803 0.038764153
## O3 -0.02102743 -0.027895099 0.048639477 -0.047559099 0.040852924
## O4 -0.08018805 0.078455271 0.007125720 -0.017702978 0.019125643
## O5 0.05146720 -0.046810133 0.023118000 0.022509445 -0.001470203
## C1 C2 C3 C4 C5
## A1 0.040294551 0.054343013 0.061619820 0.109876914 -0.018051943
## A2 -0.037395321 -0.022258789 0.134280799 -0.018992835 0.035434612
## A3 -0.002218315 -0.008485116 0.015567540 -0.003489887 -0.012961536
## A4 -0.068371314 0.187764205 -0.036279732 0.002421715 -0.127108242
## A5 0.043116099 -0.047483569 0.023230906 -0.010696224 0.017937730
## C1 0.000000000 0.284567158 0.118521806 -0.157997932 -0.039528371
## C2 0.284567158 0.000000000 0.158467547 -0.251385463 -0.052298114
## C3 0.118521806 0.158467547 0.000000000 -0.128345587 -0.190004751
## C4 -0.157997932 -0.251385463 -0.128345587 0.000000000 0.302765187
## C5 -0.039528371 -0.052298114 -0.190004751 0.302765187 0.000000000
## E1 0.036406637 0.091828153 0.033087711 0.063361274 -0.111476299
## E2 0.023913856 0.055817642 0.034701543 0.051459159 0.094176201
## E3 -0.055307712 0.050635972 -0.023172914 0.058144645 -0.051460379
## E4 0.083691517 0.026569642 -0.020502840 0.050836910 -0.017024199
## E5 0.084726643 0.092716143 0.073344851 -0.056064749 -0.041452405
## N1 -0.025897098 -0.009565368 -0.002051581 0.095683271 -0.058468007
## N2 -0.002078596 0.012955923 -0.004605731 -0.084294346 0.110337986
## N3 0.050645425 0.001455960 -0.010552713 0.033229451 0.018954601
## N4 -0.028549895 0.065312511 0.001584436 0.043422008 0.147008894
## N5 -0.012198643 0.118505422 0.034028837 0.081150342 -0.030352418
## O1 0.029780860 0.052244427 0.014329705 0.050067065 0.017342938
## O2 -0.027117739 0.068648302 0.028673405 0.133502816 0.080295312
## O3 0.048200495 0.134709913 -0.029308714 0.118288522 0.003062263
## O4 0.114615641 -0.018620893 0.041438877 0.034253946 0.092142667
## O5 -0.033568678 0.027874381 0.068369090 0.150885045 -0.024180567
## E1 E2 E3 E4 E5
## A1 0.05594849 0.022460951 0.063964807 0.068859558 0.064305748
## A2 -0.04193459 -0.038003893 -0.035863899 0.004022673 0.163432325
## A3 0.02439418 -0.025894605 0.179257763 0.057364661 -0.018008474
## A4 0.01984768 0.042126375 -0.025832709 0.134580625 -0.015764289
## A5 0.03646677 -0.019223313 0.177079886 0.236851213 0.023352938
## C1 0.03640664 0.023913856 -0.055307712 0.083691517 0.084726643
## C2 0.09182815 0.055817642 0.050635972 0.026569642 0.092716143
## C3 0.03308771 0.034701543 -0.023172914 -0.020502840 0.073344851
## C4 0.06336127 0.051459159 0.058144645 0.050836910 -0.056064749
## C5 -0.11147630 0.094176201 -0.051460379 -0.017024199 -0.041452405
## E1 0.00000000 0.262695652 -0.077544368 -0.235070586 -0.101845552
## E2 0.26269565 0.000000000 -0.088599010 -0.283971044 -0.143063885
## E3 -0.07754437 -0.088599010 0.000000000 0.106515893 0.147283742
## E4 -0.23507059 -0.283971044 0.106515893 0.000000000 -0.002266456
## E5 -0.10184555 -0.143063885 0.147283742 -0.002266456 0.000000000
## N1 -0.02349861 -0.029877221 0.010334721 -0.050727749 0.136429755
## N2 -0.04419810 0.057832274 -0.035643421 0.007463262 0.086245154
## N3 -0.01647635 -0.008541837 0.072370412 0.057514741 -0.046943225
## N4 0.12582556 0.038551939 -0.002479331 -0.099688865 -0.080652098
## N5 -0.11208989 0.141069386 -0.005501661 0.012573181 -0.099651449
## O1 0.04730387 -0.012981507 0.161675901 0.017213691 0.159084519
## O2 0.02711645 0.012344642 0.019642131 0.092844002 0.013008158
## O3 -0.07389055 -0.047272786 0.177562862 0.037968301 0.065147705
## O4 0.03789000 0.162811487 0.031197759 -0.022138419 -0.034137253
## O5 0.06637221 0.025408936 -0.011477943 0.146111122 0.001318067
## N1 N2 N3 N4 N5
## A1 0.040367713 0.055647166 0.038296693 -0.0388713311 -0.052287187
## A2 -0.070769952 0.046895017 0.013013859 0.0063692861 0.080357098
## A3 0.019636070 0.026984344 0.007005090 0.0138231298 -0.030455274
## A4 0.033789221 -0.084303811 0.052198539 -0.0689962703 0.031196672
## A5 -0.066313167 -0.045068233 -0.040611203 0.0170022205 0.043848519
## C1 -0.025897098 -0.002078596 0.050645425 -0.0285498946 -0.012198643
## C2 -0.009565368 0.012955923 0.001455960 0.0653125109 0.118505422
## C3 -0.002051581 -0.004605731 -0.010552713 0.0015844359 0.034028837
## C4 0.095683271 -0.084294346 0.033229451 0.0434220077 0.081150342
## C5 -0.058468007 0.110337986 0.018954601 0.1470088941 -0.030352418
## E1 -0.023498614 -0.044198104 -0.016476354 0.1258255597 -0.112089893
## E2 -0.029877221 0.057832274 -0.008541837 0.0385519391 0.141069386
## E3 0.010334721 -0.035643421 0.072370412 -0.0024793305 -0.005501661
## E4 -0.050727749 0.007463262 0.057514741 -0.0996888652 0.012573181
## E5 0.136429755 0.086245154 -0.046943225 -0.0806520975 -0.099651449
## N1 0.000000000 0.589748200 0.208929392 0.0677400064 0.125010691
## N2 0.589748200 0.000000000 0.199546961 0.0272499944 0.024018690
## N3 0.208929392 0.199546961 0.000000000 0.3155692584 0.165349105
## N4 0.067740006 0.027249994 0.315569258 0.0000000000 0.170490574
## N5 0.125010691 0.024018690 0.165349105 0.1704905742 0.000000000
## O1 -0.004653097 -0.026904902 -0.022917713 0.0457267810 -0.066836520
## O2 -0.020558830 0.074628217 -0.027897011 -0.0219240313 0.104087581
## O3 -0.006526932 0.012978254 -0.026167476 0.0122338201 0.004860136
## O4 -0.039419118 0.043238430 0.067372291 0.0907666231 0.029367534
## O5 0.081201606 -0.065779362 -0.013644265 -0.0009882574 0.059154246
## O1 O2 O3 O4 O5
## A1 0.076139414 0.044092425 -0.021027432 -0.080188048 0.0514672032
## A2 0.027371771 0.051742469 -0.027895099 0.078455271 -0.0468101332
## A3 -0.012405364 -0.002517178 0.048639477 0.007125720 0.0231180004
## A4 0.001681125 0.023529803 -0.047559099 -0.017702978 0.0225094451
## A5 -0.002893784 0.038764153 0.040852924 0.019125643 -0.0014702033
## C1 0.029780860 -0.027117739 0.048200495 0.114615641 -0.0335686781
## C2 0.052244427 0.068648302 0.134709913 -0.018620893 0.0278743812
## C3 0.014329705 0.028673405 -0.029308714 0.041438877 0.0683690898
## C4 0.050067065 0.133502816 0.118288522 0.034253946 0.1508850451
## C5 0.017342938 0.080295312 0.003062263 0.092142667 -0.0241805673
## E1 0.047303873 0.027116455 -0.073890547 0.037889997 0.0663722140
## E2 -0.012981507 0.012344642 -0.047272786 0.162811487 0.0254089360
## E3 0.161675901 0.019642131 0.177562862 0.031197759 -0.0114779435
## E4 0.017213691 0.092844002 0.037968301 -0.022138419 0.1461111218
## E5 0.159084519 0.013008158 0.065147705 -0.034137253 0.0013180674
## N1 -0.004653097 -0.020558830 -0.006526932 -0.039419118 0.0812016059
## N2 -0.026904902 0.074628217 0.012978254 0.043238430 -0.0657793617
## N3 -0.022917713 -0.027897011 -0.026167476 0.067372291 -0.0136442653
## N4 0.045726781 -0.021924031 0.012233820 0.090766623 -0.0009882574
## N5 -0.066836520 0.104087581 0.004860136 0.029367534 0.0591542459
## O1 0.000000000 -0.115122479 0.180775405 0.155702678 -0.1053883640
## O2 -0.115122479 0.000000000 -0.194324760 -0.002687301 0.1921171149
## O3 0.180775405 -0.194324760 0.000000000 0.144620534 -0.2013877232
## O4 0.155702678 -0.002687301 0.144620534 0.000000000 -0.1344400151
## O5 -0.105388364 0.192117115 -0.201387723 -0.134440015 0.0000000000Bootnet weight matrix:
## A1 A2 A3 A4 A5
## A1 0.00000000 -0.279043331 -0.146342179 -0.016675805 -0.031967420
## A2 -0.27904333 0.000000000 0.275803470 0.173285222 0.108863452
## A3 -0.14634218 0.275803470 0.000000000 0.156847223 0.269593707
## A4 -0.01667580 0.173285222 0.156847223 0.000000000 0.063737085
## A5 -0.03196742 0.108863452 0.269593707 0.063737085 0.000000000
## C1 0.04029455 -0.037395321 -0.002218315 -0.068371314 0.043116099
## C2 0.05434301 -0.022258789 -0.008485116 0.187764205 -0.047483569
## C3 0.06161982 0.134280799 0.015567540 -0.036279732 0.023230906
## C4 0.10987691 -0.018992835 -0.003489887 0.002421715 -0.010696224
## C5 -0.01805194 0.035434612 -0.012961536 -0.127108242 0.017937730
## E1 0.05594849 -0.041934586 0.024394176 0.019847681 0.036466766
## E2 0.02246095 -0.038003893 -0.025894605 0.042126375 -0.019223313
## E3 0.06396481 -0.035863899 0.179257763 -0.025832709 0.177079886
## E4 0.06885956 0.004022673 0.057364661 0.134580625 0.236851213
## E5 0.06430575 0.163432325 -0.018008474 -0.015764289 0.023352938
## N1 0.04036771 -0.070769952 0.019636070 0.033789221 -0.066313167
## N2 0.05564717 0.046895017 0.026984344 -0.084303811 -0.045068233
## N3 0.03829669 0.013013859 0.007005090 0.052198539 -0.040611203
## N4 -0.03887133 0.006369286 0.013823130 -0.068996270 0.017002220
## N5 -0.05228719 0.080357098 -0.030455274 0.031196672 0.043848519
## O1 0.07613941 0.027371771 -0.012405364 0.001681125 -0.002893784
## O2 0.04409243 0.051742469 -0.002517178 0.023529803 0.038764153
## O3 -0.02102743 -0.027895099 0.048639477 -0.047559099 0.040852924
## O4 -0.08018805 0.078455271 0.007125720 -0.017702978 0.019125643
## O5 0.05146720 -0.046810133 0.023118000 0.022509445 -0.001470203
## C1 C2 C3 C4 C5
## A1 0.040294551 0.054343013 0.061619820 0.109876914 -0.018051943
## A2 -0.037395321 -0.022258789 0.134280799 -0.018992835 0.035434612
## A3 -0.002218315 -0.008485116 0.015567540 -0.003489887 -0.012961536
## A4 -0.068371314 0.187764205 -0.036279732 0.002421715 -0.127108242
## A5 0.043116099 -0.047483569 0.023230906 -0.010696224 0.017937730
## C1 0.000000000 0.284567158 0.118521806 -0.157997932 -0.039528371
## C2 0.284567158 0.000000000 0.158467547 -0.251385463 -0.052298114
## C3 0.118521806 0.158467547 0.000000000 -0.128345587 -0.190004751
## C4 -0.157997932 -0.251385463 -0.128345587 0.000000000 0.302765187
## C5 -0.039528371 -0.052298114 -0.190004751 0.302765187 0.000000000
## E1 0.036406637 0.091828153 0.033087711 0.063361274 -0.111476299
## E2 0.023913856 0.055817642 0.034701543 0.051459159 0.094176201
## E3 -0.055307712 0.050635972 -0.023172914 0.058144645 -0.051460379
## E4 0.083691517 0.026569642 -0.020502840 0.050836910 -0.017024199
## E5 0.084726643 0.092716143 0.073344851 -0.056064749 -0.041452405
## N1 -0.025897098 -0.009565368 -0.002051581 0.095683271 -0.058468007
## N2 -0.002078596 0.012955923 -0.004605731 -0.084294346 0.110337986
## N3 0.050645425 0.001455960 -0.010552713 0.033229451 0.018954601
## N4 -0.028549895 0.065312511 0.001584436 0.043422008 0.147008894
## N5 -0.012198643 0.118505422 0.034028837 0.081150342 -0.030352418
## O1 0.029780860 0.052244427 0.014329705 0.050067065 0.017342938
## O2 -0.027117739 0.068648302 0.028673405 0.133502816 0.080295312
## O3 0.048200495 0.134709913 -0.029308714 0.118288522 0.003062263
## O4 0.114615641 -0.018620893 0.041438877 0.034253946 0.092142667
## O5 -0.033568678 0.027874381 0.068369090 0.150885045 -0.024180567
## E1 E2 E3 E4 E5
## A1 0.05594849 0.022460951 0.063964807 0.068859558 0.064305748
## A2 -0.04193459 -0.038003893 -0.035863899 0.004022673 0.163432325
## A3 0.02439418 -0.025894605 0.179257763 0.057364661 -0.018008474
## A4 0.01984768 0.042126375 -0.025832709 0.134580625 -0.015764289
## A5 0.03646677 -0.019223313 0.177079886 0.236851213 0.023352938
## C1 0.03640664 0.023913856 -0.055307712 0.083691517 0.084726643
## C2 0.09182815 0.055817642 0.050635972 0.026569642 0.092716143
## C3 0.03308771 0.034701543 -0.023172914 -0.020502840 0.073344851
## C4 0.06336127 0.051459159 0.058144645 0.050836910 -0.056064749
## C5 -0.11147630 0.094176201 -0.051460379 -0.017024199 -0.041452405
## E1 0.00000000 0.262695652 -0.077544368 -0.235070586 -0.101845552
## E2 0.26269565 0.000000000 -0.088599010 -0.283971044 -0.143063885
## E3 -0.07754437 -0.088599010 0.000000000 0.106515893 0.147283742
## E4 -0.23507059 -0.283971044 0.106515893 0.000000000 -0.002266456
## E5 -0.10184555 -0.143063885 0.147283742 -0.002266456 0.000000000
## N1 -0.02349861 -0.029877221 0.010334721 -0.050727749 0.136429755
## N2 -0.04419810 0.057832274 -0.035643421 0.007463262 0.086245154
## N3 -0.01647635 -0.008541837 0.072370412 0.057514741 -0.046943225
## N4 0.12582556 0.038551939 -0.002479331 -0.099688865 -0.080652098
## N5 -0.11208989 0.141069386 -0.005501661 0.012573181 -0.099651449
## O1 0.04730387 -0.012981507 0.161675901 0.017213691 0.159084519
## O2 0.02711645 0.012344642 0.019642131 0.092844002 0.013008158
## O3 -0.07389055 -0.047272786 0.177562862 0.037968301 0.065147705
## O4 0.03789000 0.162811487 0.031197759 -0.022138419 -0.034137253
## O5 0.06637221 0.025408936 -0.011477943 0.146111122 0.001318067
## N1 N2 N3 N4 N5
## A1 0.040367713 0.055647166 0.038296693 -0.0388713311 -0.052287187
## A2 -0.070769952 0.046895017 0.013013859 0.0063692861 0.080357098
## A3 0.019636070 0.026984344 0.007005090 0.0138231298 -0.030455274
## A4 0.033789221 -0.084303811 0.052198539 -0.0689962703 0.031196672
## A5 -0.066313167 -0.045068233 -0.040611203 0.0170022205 0.043848519
## C1 -0.025897098 -0.002078596 0.050645425 -0.0285498946 -0.012198643
## C2 -0.009565368 0.012955923 0.001455960 0.0653125109 0.118505422
## C3 -0.002051581 -0.004605731 -0.010552713 0.0015844359 0.034028837
## C4 0.095683271 -0.084294346 0.033229451 0.0434220077 0.081150342
## C5 -0.058468007 0.110337986 0.018954601 0.1470088941 -0.030352418
## E1 -0.023498614 -0.044198104 -0.016476354 0.1258255597 -0.112089893
## E2 -0.029877221 0.057832274 -0.008541837 0.0385519391 0.141069386
## E3 0.010334721 -0.035643421 0.072370412 -0.0024793305 -0.005501661
## E4 -0.050727749 0.007463262 0.057514741 -0.0996888652 0.012573181
## E5 0.136429755 0.086245154 -0.046943225 -0.0806520975 -0.099651449
## N1 0.000000000 0.589748200 0.208929392 0.0677400064 0.125010691
## N2 0.589748200 0.000000000 0.199546961 0.0272499944 0.024018690
## N3 0.208929392 0.199546961 0.000000000 0.3155692584 0.165349105
## N4 0.067740006 0.027249994 0.315569258 0.0000000000 0.170490574
## N5 0.125010691 0.024018690 0.165349105 0.1704905742 0.000000000
## O1 -0.004653097 -0.026904902 -0.022917713 0.0457267810 -0.066836520
## O2 -0.020558830 0.074628217 -0.027897011 -0.0219240313 0.104087581
## O3 -0.006526932 0.012978254 -0.026167476 0.0122338201 0.004860136
## O4 -0.039419118 0.043238430 0.067372291 0.0907666231 0.029367534
## O5 0.081201606 -0.065779362 -0.013644265 -0.0009882574 0.059154246
## O1 O2 O3 O4 O5
## A1 0.076139414 0.044092425 -0.021027432 -0.080188048 0.0514672032
## A2 0.027371771 0.051742469 -0.027895099 0.078455271 -0.0468101332
## A3 -0.012405364 -0.002517178 0.048639477 0.007125720 0.0231180004
## A4 0.001681125 0.023529803 -0.047559099 -0.017702978 0.0225094451
## A5 -0.002893784 0.038764153 0.040852924 0.019125643 -0.0014702033
## C1 0.029780860 -0.027117739 0.048200495 0.114615641 -0.0335686781
## C2 0.052244427 0.068648302 0.134709913 -0.018620893 0.0278743812
## C3 0.014329705 0.028673405 -0.029308714 0.041438877 0.0683690898
## C4 0.050067065 0.133502816 0.118288522 0.034253946 0.1508850451
## C5 0.017342938 0.080295312 0.003062263 0.092142667 -0.0241805673
## E1 0.047303873 0.027116455 -0.073890547 0.037889997 0.0663722140
## E2 -0.012981507 0.012344642 -0.047272786 0.162811487 0.0254089360
## E3 0.161675901 0.019642131 0.177562862 0.031197759 -0.0114779435
## E4 0.017213691 0.092844002 0.037968301 -0.022138419 0.1461111218
## E5 0.159084519 0.013008158 0.065147705 -0.034137253 0.0013180674
## N1 -0.004653097 -0.020558830 -0.006526932 -0.039419118 0.0812016059
## N2 -0.026904902 0.074628217 0.012978254 0.043238430 -0.0657793617
## N3 -0.022917713 -0.027897011 -0.026167476 0.067372291 -0.0136442653
## N4 0.045726781 -0.021924031 0.012233820 0.090766623 -0.0009882574
## N5 -0.066836520 0.104087581 0.004860136 0.029367534 0.0591542459
## O1 0.000000000 -0.115122479 0.180775405 0.155702678 -0.1053883640
## O2 -0.115122479 0.000000000 -0.194324760 -0.002687301 0.1921171149
## O3 0.180775405 -0.194324760 0.000000000 0.144620534 -0.2013877232
## O4 0.155702678 -0.002687301 0.144620534 0.000000000 -0.1344400151
## O5 -0.105388364 0.192117115 -0.201387723 -0.134440015 0.0000000000What do the arguments groups and nodeNames do?
The argument groups highlights with different colors the nodes that are assigned the same given label. The argument nodeNames is used to juxtappose descriptions to the labels, and the descriptions are then shown in the legend of the plot.
In estimateNetwork, use the threshold argument to remove all edges that are not significant after applying a bonferroni correction. Plot the resulting network.
Use the default argument in estimateNetwork to estimate a partial correlation network using glasso and EBIC model selection
Set the hypertuningparameter γ to 0. Did the network change?
Compute a thresholded regularized GGM and an unregularized GGM using these new functions, and compare your results to your previous results.
Set the default to estimate a regularized Ising model using γ = 0.5 (bootnet will automatically binarize the data for you). Compare your results with the EBIC glasso network using γ = 0.5.
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